Self-propulsion of a Quincke droplet under complex wall conditions

Currently, existing approaches to droplet self-propulsion largely rely on the superhydrophobic substrate, due to its lower adhesion force. Based on the Quincke rotation, a novel self-propulsion approach is proposed by Xie et al. [“Self-propulsion of a Quincke droplet on a superhydrophobic wall under low electric Reynolds number ReE ≤ 1,” Phys. Fluids 36, 087131 (2024)]. In this scheme, the Quincke rotation effect first allows the droplet to separate from the wall. Under the influence of the wall, the rotating movement of a droplet floating above the wall is converted into a rolling movement (rotation and translation), thus realizing the self-propulsion. It appears that the new approach relaxes the limitation of the superhydrophobic wall. Motivated by this, a two dimensional numerical study about the dynamic behaviors of droplets on the wall with varied contact angles (α) is carried out. The results show that the contact angle plays a crucial role in the activation of droplet self-propulsion. For α < 150°, a longer contact line is created, and the Quincke rotation effect gives rise to complex contact line dynamics. As α < 90°, the droplet spreads along the wall due to the rotating effect. As a result, the droplet is unable to detach from the wall and produce the self-propulsion. As 90° ≤ α < 150° (hydrophobic wall), the Quincke rotation enables the contact line to separate from the wall and achieve droplet self-propulsion. This indicates that droplet self-propulsion is no longer restricted to the superhydrophobic wall. To further expand the application of this new approach, droplet climbing on the inclined wall is also investigated. In this case, a component of the gravity (gsinβ, β is the slope of inclined wall) has two effects on the droplet behaviors: increasing droplet deformation and slowing the droplet motion. It is found that as β ≥ 20° or E*0 (dimensionless electric field strength) ≥ 27.12, the droplet cannot perform the anti-gravity motion.